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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.polynomials;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.io.Serializable;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.Arrays;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NoDataException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.analysis.ParametricUnivariateFunction;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.31"></a>
<FONT color="green">032</FONT>    <a name="line.32"></a>
<FONT color="green">033</FONT>    /**<a name="line.33"></a>
<FONT color="green">034</FONT>     * Immutable representation of a real polynomial function with real coefficients.<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;p&gt;<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;a href="http://mathworld.wolfram.com/HornersMethod.html"&gt;Horner's Method&lt;/a&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * is used to evaluate the function.&lt;/p&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     *<a name="line.38"></a>
<FONT color="green">039</FONT>     * @version $Id: PolynomialFunction.java 1383441 2012-09-11 14:56:39Z luc $<a name="line.39"></a>
<FONT color="green">040</FONT>     */<a name="line.40"></a>
<FONT color="green">041</FONT>    public class PolynomialFunction implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction, Serializable {<a name="line.41"></a>
<FONT color="green">042</FONT>        /**<a name="line.42"></a>
<FONT color="green">043</FONT>         * Serialization identifier<a name="line.43"></a>
<FONT color="green">044</FONT>         */<a name="line.44"></a>
<FONT color="green">045</FONT>        private static final long serialVersionUID = -7726511984200295583L;<a name="line.45"></a>
<FONT color="green">046</FONT>        /**<a name="line.46"></a>
<FONT color="green">047</FONT>         * The coefficients of the polynomial, ordered by degree -- i.e.,<a name="line.47"></a>
<FONT color="green">048</FONT>         * coefficients[0] is the constant term and coefficients[n] is the<a name="line.48"></a>
<FONT color="green">049</FONT>         * coefficient of x^n where n is the degree of the polynomial.<a name="line.49"></a>
<FONT color="green">050</FONT>         */<a name="line.50"></a>
<FONT color="green">051</FONT>        private final double coefficients[];<a name="line.51"></a>
<FONT color="green">052</FONT>    <a name="line.52"></a>
<FONT color="green">053</FONT>        /**<a name="line.53"></a>
<FONT color="green">054</FONT>         * Construct a polynomial with the given coefficients.  The first element<a name="line.54"></a>
<FONT color="green">055</FONT>         * of the coefficients array is the constant term.  Higher degree<a name="line.55"></a>
<FONT color="green">056</FONT>         * coefficients follow in sequence.  The degree of the resulting polynomial<a name="line.56"></a>
<FONT color="green">057</FONT>         * is the index of the last non-null element of the array, or 0 if all elements<a name="line.57"></a>
<FONT color="green">058</FONT>         * are null.<a name="line.58"></a>
<FONT color="green">059</FONT>         * &lt;p&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>         * The constructor makes a copy of the input array and assigns the copy to<a name="line.60"></a>
<FONT color="green">061</FONT>         * the coefficients property.&lt;/p&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>         *<a name="line.62"></a>
<FONT color="green">063</FONT>         * @param c Polynomial coefficients.<a name="line.63"></a>
<FONT color="green">064</FONT>         * @throws NullArgumentException if {@code c} is {@code null}.<a name="line.64"></a>
<FONT color="green">065</FONT>         * @throws NoDataException if {@code c} is empty.<a name="line.65"></a>
<FONT color="green">066</FONT>         */<a name="line.66"></a>
<FONT color="green">067</FONT>        public PolynomialFunction(double c[])<a name="line.67"></a>
<FONT color="green">068</FONT>            throws NullArgumentException, NoDataException {<a name="line.68"></a>
<FONT color="green">069</FONT>            super();<a name="line.69"></a>
<FONT color="green">070</FONT>            MathUtils.checkNotNull(c);<a name="line.70"></a>
<FONT color="green">071</FONT>            int n = c.length;<a name="line.71"></a>
<FONT color="green">072</FONT>            if (n == 0) {<a name="line.72"></a>
<FONT color="green">073</FONT>                throw new NoDataException(LocalizedFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);<a name="line.73"></a>
<FONT color="green">074</FONT>            }<a name="line.74"></a>
<FONT color="green">075</FONT>            while ((n &gt; 1) &amp;&amp; (c[n - 1] == 0)) {<a name="line.75"></a>
<FONT color="green">076</FONT>                --n;<a name="line.76"></a>
<FONT color="green">077</FONT>            }<a name="line.77"></a>
<FONT color="green">078</FONT>            this.coefficients = new double[n];<a name="line.78"></a>
<FONT color="green">079</FONT>            System.arraycopy(c, 0, this.coefficients, 0, n);<a name="line.79"></a>
<FONT color="green">080</FONT>        }<a name="line.80"></a>
<FONT color="green">081</FONT>    <a name="line.81"></a>
<FONT color="green">082</FONT>        /**<a name="line.82"></a>
<FONT color="green">083</FONT>         * Compute the value of the function for the given argument.<a name="line.83"></a>
<FONT color="green">084</FONT>         * &lt;p&gt;<a name="line.84"></a>
<FONT color="green">085</FONT>         *  The value returned is &lt;br/&gt;<a name="line.85"></a>
<FONT color="green">086</FONT>         *  &lt;code&gt;coefficients[n] * x^n + ... + coefficients[1] * x  + coefficients[0]&lt;/code&gt;<a name="line.86"></a>
<FONT color="green">087</FONT>         * &lt;/p&gt;<a name="line.87"></a>
<FONT color="green">088</FONT>         *<a name="line.88"></a>
<FONT color="green">089</FONT>         * @param x Argument for which the function value should be computed.<a name="line.89"></a>
<FONT color="green">090</FONT>         * @return the value of the polynomial at the given point.<a name="line.90"></a>
<FONT color="green">091</FONT>         * @see UnivariateFunction#value(double)<a name="line.91"></a>
<FONT color="green">092</FONT>         */<a name="line.92"></a>
<FONT color="green">093</FONT>        public double value(double x) {<a name="line.93"></a>
<FONT color="green">094</FONT>           return evaluate(coefficients, x);<a name="line.94"></a>
<FONT color="green">095</FONT>        }<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>        /**<a name="line.97"></a>
<FONT color="green">098</FONT>         * Returns the degree of the polynomial.<a name="line.98"></a>
<FONT color="green">099</FONT>         *<a name="line.99"></a>
<FONT color="green">100</FONT>         * @return the degree of the polynomial.<a name="line.100"></a>
<FONT color="green">101</FONT>         */<a name="line.101"></a>
<FONT color="green">102</FONT>        public int degree() {<a name="line.102"></a>
<FONT color="green">103</FONT>            return coefficients.length - 1;<a name="line.103"></a>
<FONT color="green">104</FONT>        }<a name="line.104"></a>
<FONT color="green">105</FONT>    <a name="line.105"></a>
<FONT color="green">106</FONT>        /**<a name="line.106"></a>
<FONT color="green">107</FONT>         * Returns a copy of the coefficients array.<a name="line.107"></a>
<FONT color="green">108</FONT>         * &lt;p&gt;<a name="line.108"></a>
<FONT color="green">109</FONT>         * Changes made to the returned copy will not affect the coefficients of<a name="line.109"></a>
<FONT color="green">110</FONT>         * the polynomial.&lt;/p&gt;<a name="line.110"></a>
<FONT color="green">111</FONT>         *<a name="line.111"></a>
<FONT color="green">112</FONT>         * @return a fresh copy of the coefficients array.<a name="line.112"></a>
<FONT color="green">113</FONT>         */<a name="line.113"></a>
<FONT color="green">114</FONT>        public double[] getCoefficients() {<a name="line.114"></a>
<FONT color="green">115</FONT>            return coefficients.clone();<a name="line.115"></a>
<FONT color="green">116</FONT>        }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>        /**<a name="line.118"></a>
<FONT color="green">119</FONT>         * Uses Horner's Method to evaluate the polynomial with the given coefficients at<a name="line.119"></a>
<FONT color="green">120</FONT>         * the argument.<a name="line.120"></a>
<FONT color="green">121</FONT>         *<a name="line.121"></a>
<FONT color="green">122</FONT>         * @param coefficients Coefficients of the polynomial to evaluate.<a name="line.122"></a>
<FONT color="green">123</FONT>         * @param argument Input value.<a name="line.123"></a>
<FONT color="green">124</FONT>         * @return the value of the polynomial.<a name="line.124"></a>
<FONT color="green">125</FONT>         * @throws NoDataException if {@code coefficients} is empty.<a name="line.125"></a>
<FONT color="green">126</FONT>         * @throws NullArgumentException if {@code coefficients} is {@code null}.<a name="line.126"></a>
<FONT color="green">127</FONT>         */<a name="line.127"></a>
<FONT color="green">128</FONT>        protected static double evaluate(double[] coefficients, double argument)<a name="line.128"></a>
<FONT color="green">129</FONT>            throws NullArgumentException, NoDataException {<a name="line.129"></a>
<FONT color="green">130</FONT>            MathUtils.checkNotNull(coefficients);<a name="line.130"></a>
<FONT color="green">131</FONT>            int n = coefficients.length;<a name="line.131"></a>
<FONT color="green">132</FONT>            if (n == 0) {<a name="line.132"></a>
<FONT color="green">133</FONT>                throw new NoDataException(LocalizedFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);<a name="line.133"></a>
<FONT color="green">134</FONT>            }<a name="line.134"></a>
<FONT color="green">135</FONT>            double result = coefficients[n - 1];<a name="line.135"></a>
<FONT color="green">136</FONT>            for (int j = n - 2; j &gt;= 0; j--) {<a name="line.136"></a>
<FONT color="green">137</FONT>                result = argument * result + coefficients[j];<a name="line.137"></a>
<FONT color="green">138</FONT>            }<a name="line.138"></a>
<FONT color="green">139</FONT>            return result;<a name="line.139"></a>
<FONT color="green">140</FONT>        }<a name="line.140"></a>
<FONT color="green">141</FONT>    <a name="line.141"></a>
<FONT color="green">142</FONT>    <a name="line.142"></a>
<FONT color="green">143</FONT>        /** {@inheritDoc}<a name="line.143"></a>
<FONT color="green">144</FONT>         * @since 3.1<a name="line.144"></a>
<FONT color="green">145</FONT>         * @throws NoDataException if {@code coefficients} is empty.<a name="line.145"></a>
<FONT color="green">146</FONT>         * @throws NullArgumentException if {@code coefficients} is {@code null}.<a name="line.146"></a>
<FONT color="green">147</FONT>         */<a name="line.147"></a>
<FONT color="green">148</FONT>        public DerivativeStructure value(final DerivativeStructure t)<a name="line.148"></a>
<FONT color="green">149</FONT>            throws NullArgumentException, NoDataException {<a name="line.149"></a>
<FONT color="green">150</FONT>            MathUtils.checkNotNull(coefficients);<a name="line.150"></a>
<FONT color="green">151</FONT>            int n = coefficients.length;<a name="line.151"></a>
<FONT color="green">152</FONT>            if (n == 0) {<a name="line.152"></a>
<FONT color="green">153</FONT>                throw new NoDataException(LocalizedFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);<a name="line.153"></a>
<FONT color="green">154</FONT>            }<a name="line.154"></a>
<FONT color="green">155</FONT>            DerivativeStructure result =<a name="line.155"></a>
<FONT color="green">156</FONT>                    new DerivativeStructure(t.getFreeParameters(), t.getOrder(), coefficients[n - 1]);<a name="line.156"></a>
<FONT color="green">157</FONT>            for (int j = n - 2; j &gt;= 0; j--) {<a name="line.157"></a>
<FONT color="green">158</FONT>                result = result.multiply(t).add(coefficients[j]);<a name="line.158"></a>
<FONT color="green">159</FONT>            }<a name="line.159"></a>
<FONT color="green">160</FONT>            return result;<a name="line.160"></a>
<FONT color="green">161</FONT>        }<a name="line.161"></a>
<FONT color="green">162</FONT>    <a name="line.162"></a>
<FONT color="green">163</FONT>        /**<a name="line.163"></a>
<FONT color="green">164</FONT>         * Add a polynomial to the instance.<a name="line.164"></a>
<FONT color="green">165</FONT>         *<a name="line.165"></a>
<FONT color="green">166</FONT>         * @param p Polynomial to add.<a name="line.166"></a>
<FONT color="green">167</FONT>         * @return a new polynomial which is the sum of the instance and {@code p}.<a name="line.167"></a>
<FONT color="green">168</FONT>         */<a name="line.168"></a>
<FONT color="green">169</FONT>        public PolynomialFunction add(final PolynomialFunction p) {<a name="line.169"></a>
<FONT color="green">170</FONT>            // identify the lowest degree polynomial<a name="line.170"></a>
<FONT color="green">171</FONT>            final int lowLength  = FastMath.min(coefficients.length, p.coefficients.length);<a name="line.171"></a>
<FONT color="green">172</FONT>            final int highLength = FastMath.max(coefficients.length, p.coefficients.length);<a name="line.172"></a>
<FONT color="green">173</FONT>    <a name="line.173"></a>
<FONT color="green">174</FONT>            // build the coefficients array<a name="line.174"></a>
<FONT color="green">175</FONT>            double[] newCoefficients = new double[highLength];<a name="line.175"></a>
<FONT color="green">176</FONT>            for (int i = 0; i &lt; lowLength; ++i) {<a name="line.176"></a>
<FONT color="green">177</FONT>                newCoefficients[i] = coefficients[i] + p.coefficients[i];<a name="line.177"></a>
<FONT color="green">178</FONT>            }<a name="line.178"></a>
<FONT color="green">179</FONT>            System.arraycopy((coefficients.length &lt; p.coefficients.length) ?<a name="line.179"></a>
<FONT color="green">180</FONT>                             p.coefficients : coefficients,<a name="line.180"></a>
<FONT color="green">181</FONT>                             lowLength,<a name="line.181"></a>
<FONT color="green">182</FONT>                             newCoefficients, lowLength,<a name="line.182"></a>
<FONT color="green">183</FONT>                             highLength - lowLength);<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>            return new PolynomialFunction(newCoefficients);<a name="line.185"></a>
<FONT color="green">186</FONT>        }<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>        /**<a name="line.188"></a>
<FONT color="green">189</FONT>         * Subtract a polynomial from the instance.<a name="line.189"></a>
<FONT color="green">190</FONT>         *<a name="line.190"></a>
<FONT color="green">191</FONT>         * @param p Polynomial to subtract.<a name="line.191"></a>
<FONT color="green">192</FONT>         * @return a new polynomial which is the difference the instance minus {@code p}.<a name="line.192"></a>
<FONT color="green">193</FONT>         */<a name="line.193"></a>
<FONT color="green">194</FONT>        public PolynomialFunction subtract(final PolynomialFunction p) {<a name="line.194"></a>
<FONT color="green">195</FONT>            // identify the lowest degree polynomial<a name="line.195"></a>
<FONT color="green">196</FONT>            int lowLength  = FastMath.min(coefficients.length, p.coefficients.length);<a name="line.196"></a>
<FONT color="green">197</FONT>            int highLength = FastMath.max(coefficients.length, p.coefficients.length);<a name="line.197"></a>
<FONT color="green">198</FONT>    <a name="line.198"></a>
<FONT color="green">199</FONT>            // build the coefficients array<a name="line.199"></a>
<FONT color="green">200</FONT>            double[] newCoefficients = new double[highLength];<a name="line.200"></a>
<FONT color="green">201</FONT>            for (int i = 0; i &lt; lowLength; ++i) {<a name="line.201"></a>
<FONT color="green">202</FONT>                newCoefficients[i] = coefficients[i] - p.coefficients[i];<a name="line.202"></a>
<FONT color="green">203</FONT>            }<a name="line.203"></a>
<FONT color="green">204</FONT>            if (coefficients.length &lt; p.coefficients.length) {<a name="line.204"></a>
<FONT color="green">205</FONT>                for (int i = lowLength; i &lt; highLength; ++i) {<a name="line.205"></a>
<FONT color="green">206</FONT>                    newCoefficients[i] = -p.coefficients[i];<a name="line.206"></a>
<FONT color="green">207</FONT>                }<a name="line.207"></a>
<FONT color="green">208</FONT>            } else {<a name="line.208"></a>
<FONT color="green">209</FONT>                System.arraycopy(coefficients, lowLength, newCoefficients, lowLength,<a name="line.209"></a>
<FONT color="green">210</FONT>                                 highLength - lowLength);<a name="line.210"></a>
<FONT color="green">211</FONT>            }<a name="line.211"></a>
<FONT color="green">212</FONT>    <a name="line.212"></a>
<FONT color="green">213</FONT>            return new PolynomialFunction(newCoefficients);<a name="line.213"></a>
<FONT color="green">214</FONT>        }<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>        /**<a name="line.216"></a>
<FONT color="green">217</FONT>         * Negate the instance.<a name="line.217"></a>
<FONT color="green">218</FONT>         *<a name="line.218"></a>
<FONT color="green">219</FONT>         * @return a new polynomial.<a name="line.219"></a>
<FONT color="green">220</FONT>         */<a name="line.220"></a>
<FONT color="green">221</FONT>        public PolynomialFunction negate() {<a name="line.221"></a>
<FONT color="green">222</FONT>            double[] newCoefficients = new double[coefficients.length];<a name="line.222"></a>
<FONT color="green">223</FONT>            for (int i = 0; i &lt; coefficients.length; ++i) {<a name="line.223"></a>
<FONT color="green">224</FONT>                newCoefficients[i] = -coefficients[i];<a name="line.224"></a>
<FONT color="green">225</FONT>            }<a name="line.225"></a>
<FONT color="green">226</FONT>            return new PolynomialFunction(newCoefficients);<a name="line.226"></a>
<FONT color="green">227</FONT>        }<a name="line.227"></a>
<FONT color="green">228</FONT>    <a name="line.228"></a>
<FONT color="green">229</FONT>        /**<a name="line.229"></a>
<FONT color="green">230</FONT>         * Multiply the instance by a polynomial.<a name="line.230"></a>
<FONT color="green">231</FONT>         *<a name="line.231"></a>
<FONT color="green">232</FONT>         * @param p Polynomial to multiply by.<a name="line.232"></a>
<FONT color="green">233</FONT>         * @return a new polynomial.<a name="line.233"></a>
<FONT color="green">234</FONT>         */<a name="line.234"></a>
<FONT color="green">235</FONT>        public PolynomialFunction multiply(final PolynomialFunction p) {<a name="line.235"></a>
<FONT color="green">236</FONT>            double[] newCoefficients = new double[coefficients.length + p.coefficients.length - 1];<a name="line.236"></a>
<FONT color="green">237</FONT>    <a name="line.237"></a>
<FONT color="green">238</FONT>            for (int i = 0; i &lt; newCoefficients.length; ++i) {<a name="line.238"></a>
<FONT color="green">239</FONT>                newCoefficients[i] = 0.0;<a name="line.239"></a>
<FONT color="green">240</FONT>                for (int j = FastMath.max(0, i + 1 - p.coefficients.length);<a name="line.240"></a>
<FONT color="green">241</FONT>                     j &lt; FastMath.min(coefficients.length, i + 1);<a name="line.241"></a>
<FONT color="green">242</FONT>                     ++j) {<a name="line.242"></a>
<FONT color="green">243</FONT>                    newCoefficients[i] += coefficients[j] * p.coefficients[i-j];<a name="line.243"></a>
<FONT color="green">244</FONT>                }<a name="line.244"></a>
<FONT color="green">245</FONT>            }<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>            return new PolynomialFunction(newCoefficients);<a name="line.247"></a>
<FONT color="green">248</FONT>        }<a name="line.248"></a>
<FONT color="green">249</FONT>    <a name="line.249"></a>
<FONT color="green">250</FONT>        /**<a name="line.250"></a>
<FONT color="green">251</FONT>         * Returns the coefficients of the derivative of the polynomial with the given coefficients.<a name="line.251"></a>
<FONT color="green">252</FONT>         *<a name="line.252"></a>
<FONT color="green">253</FONT>         * @param coefficients Coefficients of the polynomial to differentiate.<a name="line.253"></a>
<FONT color="green">254</FONT>         * @return the coefficients of the derivative or {@code null} if coefficients has length 1.<a name="line.254"></a>
<FONT color="green">255</FONT>         * @throws NoDataException if {@code coefficients} is empty.<a name="line.255"></a>
<FONT color="green">256</FONT>         * @throws NullArgumentException if {@code coefficients} is {@code null}.<a name="line.256"></a>
<FONT color="green">257</FONT>         */<a name="line.257"></a>
<FONT color="green">258</FONT>        protected static double[] differentiate(double[] coefficients)<a name="line.258"></a>
<FONT color="green">259</FONT>            throws NullArgumentException, NoDataException {<a name="line.259"></a>
<FONT color="green">260</FONT>            MathUtils.checkNotNull(coefficients);<a name="line.260"></a>
<FONT color="green">261</FONT>            int n = coefficients.length;<a name="line.261"></a>
<FONT color="green">262</FONT>            if (n == 0) {<a name="line.262"></a>
<FONT color="green">263</FONT>                throw new NoDataException(LocalizedFormats.EMPTY_POLYNOMIALS_COEFFICIENTS_ARRAY);<a name="line.263"></a>
<FONT color="green">264</FONT>            }<a name="line.264"></a>
<FONT color="green">265</FONT>            if (n == 1) {<a name="line.265"></a>
<FONT color="green">266</FONT>                return new double[]{0};<a name="line.266"></a>
<FONT color="green">267</FONT>            }<a name="line.267"></a>
<FONT color="green">268</FONT>            double[] result = new double[n - 1];<a name="line.268"></a>
<FONT color="green">269</FONT>            for (int i = n - 1; i &gt; 0; i--) {<a name="line.269"></a>
<FONT color="green">270</FONT>                result[i - 1] = i * coefficients[i];<a name="line.270"></a>
<FONT color="green">271</FONT>            }<a name="line.271"></a>
<FONT color="green">272</FONT>            return result;<a name="line.272"></a>
<FONT color="green">273</FONT>        }<a name="line.273"></a>
<FONT color="green">274</FONT>    <a name="line.274"></a>
<FONT color="green">275</FONT>        /**<a name="line.275"></a>
<FONT color="green">276</FONT>         * Returns the derivative as a {@link PolynomialFunction}.<a name="line.276"></a>
<FONT color="green">277</FONT>         *<a name="line.277"></a>
<FONT color="green">278</FONT>         * @return the derivative polynomial.<a name="line.278"></a>
<FONT color="green">279</FONT>         */<a name="line.279"></a>
<FONT color="green">280</FONT>        public PolynomialFunction polynomialDerivative() {<a name="line.280"></a>
<FONT color="green">281</FONT>            return new PolynomialFunction(differentiate(coefficients));<a name="line.281"></a>
<FONT color="green">282</FONT>        }<a name="line.282"></a>
<FONT color="green">283</FONT>    <a name="line.283"></a>
<FONT color="green">284</FONT>        /**<a name="line.284"></a>
<FONT color="green">285</FONT>         * Returns the derivative as a {@link UnivariateFunction}.<a name="line.285"></a>
<FONT color="green">286</FONT>         *<a name="line.286"></a>
<FONT color="green">287</FONT>         * @return the derivative function.<a name="line.287"></a>
<FONT color="green">288</FONT>         */<a name="line.288"></a>
<FONT color="green">289</FONT>        public UnivariateFunction derivative() {<a name="line.289"></a>
<FONT color="green">290</FONT>            return polynomialDerivative();<a name="line.290"></a>
<FONT color="green">291</FONT>        }<a name="line.291"></a>
<FONT color="green">292</FONT>    <a name="line.292"></a>
<FONT color="green">293</FONT>        /**<a name="line.293"></a>
<FONT color="green">294</FONT>         * Returns a string representation of the polynomial.<a name="line.294"></a>
<FONT color="green">295</FONT>         *<a name="line.295"></a>
<FONT color="green">296</FONT>         * &lt;p&gt;The representation is user oriented. Terms are displayed lowest<a name="line.296"></a>
<FONT color="green">297</FONT>         * degrees first. The multiplications signs, coefficients equals to<a name="line.297"></a>
<FONT color="green">298</FONT>         * one and null terms are not displayed (except if the polynomial is 0,<a name="line.298"></a>
<FONT color="green">299</FONT>         * in which case the 0 constant term is displayed). Addition of terms<a name="line.299"></a>
<FONT color="green">300</FONT>         * with negative coefficients are replaced by subtraction of terms<a name="line.300"></a>
<FONT color="green">301</FONT>         * with positive coefficients except for the first displayed term<a name="line.301"></a>
<FONT color="green">302</FONT>         * (i.e. we display &lt;code&gt;-3&lt;/code&gt; for a constant negative polynomial,<a name="line.302"></a>
<FONT color="green">303</FONT>         * but &lt;code&gt;1 - 3 x + x^2&lt;/code&gt; if the negative coefficient is not<a name="line.303"></a>
<FONT color="green">304</FONT>         * the first one displayed).&lt;/p&gt;<a name="line.304"></a>
<FONT color="green">305</FONT>         *<a name="line.305"></a>
<FONT color="green">306</FONT>         * @return a string representation of the polynomial.<a name="line.306"></a>
<FONT color="green">307</FONT>         */<a name="line.307"></a>
<FONT color="green">308</FONT>        @Override<a name="line.308"></a>
<FONT color="green">309</FONT>        public String toString() {<a name="line.309"></a>
<FONT color="green">310</FONT>            StringBuilder s = new StringBuilder();<a name="line.310"></a>
<FONT color="green">311</FONT>            if (coefficients[0] == 0.0) {<a name="line.311"></a>
<FONT color="green">312</FONT>                if (coefficients.length == 1) {<a name="line.312"></a>
<FONT color="green">313</FONT>                    return "0";<a name="line.313"></a>
<FONT color="green">314</FONT>                }<a name="line.314"></a>
<FONT color="green">315</FONT>            } else {<a name="line.315"></a>
<FONT color="green">316</FONT>                s.append(toString(coefficients[0]));<a name="line.316"></a>
<FONT color="green">317</FONT>            }<a name="line.317"></a>
<FONT color="green">318</FONT>    <a name="line.318"></a>
<FONT color="green">319</FONT>            for (int i = 1; i &lt; coefficients.length; ++i) {<a name="line.319"></a>
<FONT color="green">320</FONT>                if (coefficients[i] != 0) {<a name="line.320"></a>
<FONT color="green">321</FONT>                    if (s.length() &gt; 0) {<a name="line.321"></a>
<FONT color="green">322</FONT>                        if (coefficients[i] &lt; 0) {<a name="line.322"></a>
<FONT color="green">323</FONT>                            s.append(" - ");<a name="line.323"></a>
<FONT color="green">324</FONT>                        } else {<a name="line.324"></a>
<FONT color="green">325</FONT>                            s.append(" + ");<a name="line.325"></a>
<FONT color="green">326</FONT>                        }<a name="line.326"></a>
<FONT color="green">327</FONT>                    } else {<a name="line.327"></a>
<FONT color="green">328</FONT>                        if (coefficients[i] &lt; 0) {<a name="line.328"></a>
<FONT color="green">329</FONT>                            s.append("-");<a name="line.329"></a>
<FONT color="green">330</FONT>                        }<a name="line.330"></a>
<FONT color="green">331</FONT>                    }<a name="line.331"></a>
<FONT color="green">332</FONT>    <a name="line.332"></a>
<FONT color="green">333</FONT>                    double absAi = FastMath.abs(coefficients[i]);<a name="line.333"></a>
<FONT color="green">334</FONT>                    if ((absAi - 1) != 0) {<a name="line.334"></a>
<FONT color="green">335</FONT>                        s.append(toString(absAi));<a name="line.335"></a>
<FONT color="green">336</FONT>                        s.append(' ');<a name="line.336"></a>
<FONT color="green">337</FONT>                    }<a name="line.337"></a>
<FONT color="green">338</FONT>    <a name="line.338"></a>
<FONT color="green">339</FONT>                    s.append("x");<a name="line.339"></a>
<FONT color="green">340</FONT>                    if (i &gt; 1) {<a name="line.340"></a>
<FONT color="green">341</FONT>                        s.append('^');<a name="line.341"></a>
<FONT color="green">342</FONT>                        s.append(Integer.toString(i));<a name="line.342"></a>
<FONT color="green">343</FONT>                    }<a name="line.343"></a>
<FONT color="green">344</FONT>                }<a name="line.344"></a>
<FONT color="green">345</FONT>            }<a name="line.345"></a>
<FONT color="green">346</FONT>    <a name="line.346"></a>
<FONT color="green">347</FONT>            return s.toString();<a name="line.347"></a>
<FONT color="green">348</FONT>        }<a name="line.348"></a>
<FONT color="green">349</FONT>    <a name="line.349"></a>
<FONT color="green">350</FONT>        /**<a name="line.350"></a>
<FONT color="green">351</FONT>         * Creates a string representing a coefficient, removing ".0" endings.<a name="line.351"></a>
<FONT color="green">352</FONT>         *<a name="line.352"></a>
<FONT color="green">353</FONT>         * @param coeff Coefficient.<a name="line.353"></a>
<FONT color="green">354</FONT>         * @return a string representation of {@code coeff}.<a name="line.354"></a>
<FONT color="green">355</FONT>         */<a name="line.355"></a>
<FONT color="green">356</FONT>        private static String toString(double coeff) {<a name="line.356"></a>
<FONT color="green">357</FONT>            final String c = Double.toString(coeff);<a name="line.357"></a>
<FONT color="green">358</FONT>            if (c.endsWith(".0")) {<a name="line.358"></a>
<FONT color="green">359</FONT>                return c.substring(0, c.length() - 2);<a name="line.359"></a>
<FONT color="green">360</FONT>            } else {<a name="line.360"></a>
<FONT color="green">361</FONT>                return c;<a name="line.361"></a>
<FONT color="green">362</FONT>            }<a name="line.362"></a>
<FONT color="green">363</FONT>        }<a name="line.363"></a>
<FONT color="green">364</FONT>    <a name="line.364"></a>
<FONT color="green">365</FONT>        /** {@inheritDoc} */<a name="line.365"></a>
<FONT color="green">366</FONT>        @Override<a name="line.366"></a>
<FONT color="green">367</FONT>        public int hashCode() {<a name="line.367"></a>
<FONT color="green">368</FONT>            final int prime = 31;<a name="line.368"></a>
<FONT color="green">369</FONT>            int result = 1;<a name="line.369"></a>
<FONT color="green">370</FONT>            result = prime * result + Arrays.hashCode(coefficients);<a name="line.370"></a>
<FONT color="green">371</FONT>            return result;<a name="line.371"></a>
<FONT color="green">372</FONT>        }<a name="line.372"></a>
<FONT color="green">373</FONT>    <a name="line.373"></a>
<FONT color="green">374</FONT>        /** {@inheritDoc} */<a name="line.374"></a>
<FONT color="green">375</FONT>        @Override<a name="line.375"></a>
<FONT color="green">376</FONT>        public boolean equals(Object obj) {<a name="line.376"></a>
<FONT color="green">377</FONT>            if (this == obj) {<a name="line.377"></a>
<FONT color="green">378</FONT>                return true;<a name="line.378"></a>
<FONT color="green">379</FONT>            }<a name="line.379"></a>
<FONT color="green">380</FONT>            if (!(obj instanceof PolynomialFunction)) {<a name="line.380"></a>
<FONT color="green">381</FONT>                return false;<a name="line.381"></a>
<FONT color="green">382</FONT>            }<a name="line.382"></a>
<FONT color="green">383</FONT>            PolynomialFunction other = (PolynomialFunction) obj;<a name="line.383"></a>
<FONT color="green">384</FONT>            if (!Arrays.equals(coefficients, other.coefficients)) {<a name="line.384"></a>
<FONT color="green">385</FONT>                return false;<a name="line.385"></a>
<FONT color="green">386</FONT>            }<a name="line.386"></a>
<FONT color="green">387</FONT>            return true;<a name="line.387"></a>
<FONT color="green">388</FONT>        }<a name="line.388"></a>
<FONT color="green">389</FONT>    <a name="line.389"></a>
<FONT color="green">390</FONT>        /**<a name="line.390"></a>
<FONT color="green">391</FONT>         * Dedicated parametric polynomial class.<a name="line.391"></a>
<FONT color="green">392</FONT>         *<a name="line.392"></a>
<FONT color="green">393</FONT>         * @since 3.0<a name="line.393"></a>
<FONT color="green">394</FONT>         */<a name="line.394"></a>
<FONT color="green">395</FONT>        public static class Parametric implements ParametricUnivariateFunction {<a name="line.395"></a>
<FONT color="green">396</FONT>            /** {@inheritDoc} */<a name="line.396"></a>
<FONT color="green">397</FONT>            public double[] gradient(double x, double ... parameters) {<a name="line.397"></a>
<FONT color="green">398</FONT>                final double[] gradient = new double[parameters.length];<a name="line.398"></a>
<FONT color="green">399</FONT>                double xn = 1.0;<a name="line.399"></a>
<FONT color="green">400</FONT>                for (int i = 0; i &lt; parameters.length; ++i) {<a name="line.400"></a>
<FONT color="green">401</FONT>                    gradient[i] = xn;<a name="line.401"></a>
<FONT color="green">402</FONT>                    xn *= x;<a name="line.402"></a>
<FONT color="green">403</FONT>                }<a name="line.403"></a>
<FONT color="green">404</FONT>                return gradient;<a name="line.404"></a>
<FONT color="green">405</FONT>            }<a name="line.405"></a>
<FONT color="green">406</FONT>    <a name="line.406"></a>
<FONT color="green">407</FONT>            /** {@inheritDoc} */<a name="line.407"></a>
<FONT color="green">408</FONT>            public double value(final double x, final double ... parameters) {<a name="line.408"></a>
<FONT color="green">409</FONT>                return PolynomialFunction.evaluate(parameters, x);<a name="line.409"></a>
<FONT color="green">410</FONT>            }<a name="line.410"></a>
<FONT color="green">411</FONT>        }<a name="line.411"></a>
<FONT color="green">412</FONT>    }<a name="line.412"></a>




























































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